Determine, without graphing, whether the given quadratic function has a maximum value or a minimum value and then
find that value.
-$$f ( x ) = x ^ { 2 } + 2$$
A) minimum; 0
B) minimum; 2
C) maximum; 2
D) maximum; 0

Question

Quizplus · Accepted Answer

The given quadratic function $f(x) = x^2 + 2$ is in the form $ax^2 + bx + c$ with $a = 1$, $b = 0$, and $c = 2$. Since $a > 0$, the parabola opens upwards, indicating a minimum value. The vertex form of a parabola is $f(x) = a(x - h)^2 + k$, where $(h, k)$ is the vertex. For $f(x) = x^2 + 2$, the vertex is at $(0, 2)$, thus the minimum value is 2.

Determine, Without Graphing, Whether the Given Quadratic Function Has a Maximum